Suppose you are testing the following claim: "More than 47% of car crashes occur within 2 miles of the motorists home." Express the null and alternative hypotheses in symbolic form for a hypothesis test (enter as a percentage).
H0:pH0:p (Enter percentages, not decimals. Example 99%, not 0.99)
Ha:pHa:p (Enter percentages, not decimals. Example 99%, not 0.99)
Use the following codes to enter the following symbols:
≥≥ enter >=
>> enter >
≤≤ enter <=
<< enter <
≠≠ enter !=

Answer: 0.00003396739

Step-by-step explanation:

hope this helps

The x-values that are excluded from the solution set of the rational equation are those that would make the denominator of any of the fractions equal to zero. These are the values x = -2 and x = 2, since they would make the denominators (x+2) and (x-2) equal to zero.

To solve the equation for x, we can first find a common denominator for all the fractions and then combine them into one fraction:

(2)/(x+2)=(3)/(x-2)-(7)/((x+2)(x-2))

Multiply both sides of the equation by the common denominator (x+2)(x-2) to eliminate the fractions

:2(x+2)(x-2) = 3(x+2)(x-2) - 7

Distribute the terms:

2x^2 - 8 = 3x^2 - 12x + 12 - 7

Combine like terms and rearrange the equation:

x^2 - 12x + 13 = 0

Use the quadratic formula to find the values of x:

x = (-b ± √(b^2 - 4ac))/(2a) = (-(-12) ± √((-12)^2 - 4(1)(13)))/(2(1)) = (12 ± √(144 - 52))/(2) = (12 ± √92)/(2) = (12 ± 2√23)/(2) = 6 ± √23

Therefore, the solutions for x are 6 + √23 and 6 - √23.

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The other three angle measures in the quadrilateral, in addition to <1 = 45 degrees, are: <2 = <3 = 135 degrees, and <4 = 45 degrees.

What is the quadrilateral?

A quadrilateral is a polygon with four sides and four angles. In other words, it is a closed figure that has four straight sides and four vertices (corners).

If <1 has a measure of 45 degrees, then the sum of the angle measures in the quadrilateral must be 360 degrees. Let's call the other three angles in the quadrilateral <2, <3, and <4.

Then we can use the fact that the opposite angles in a quadrilateral add up to 180 degrees to write two equations:

<1 + <3 = 180 (opposite angles)

<2 + <4 = 180 (opposite angles)

We also know that <1 = 45, so we can substitute that in the first equation:

45 + <3 = 180

Solving for <3, we get:

<3 = 135

Now we can substitute the values of <1 and <3 into the sum of angle measures equation:

45 + <2 + 135 + <4 = 360

Simplifying, we get:

<2 + <4 = 180

This is the same equation as the opposite angles equation, so we know that <2 and <4 are also opposite angles. Therefore, we can conclude that:

<2 = <3 = 135 degrees

<4 = 45 degrees

Hence, the other three angle measures in the quadrilateral, in addition to <1 = 45 degrees, are: <2 = <3 = 135 degrees, and <4 = 45 degrees.

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Using composition function , the price of the computer after both discounts are applied is 0.7x - 140.

To find the price of the computer after both discounts are applied, we can use composition function . Specifically, we can find the composition of f and g, denoted as f(g(x)) or (f o g)(x). This will give us the price of the computer after both discounts are applied.

To find f(g(x)), we can substitute the expression for g(x) into the function f(x):

f(g(x)) = f(0.7x) = (0.7x) - 200

So the price of the computer after both discounts are applied is (0.7x) - 200.

Alternatively, we could find the composition of g and f, denoted as g(f(x)) or (g o f)(x). This will give us the same result, since the order of the discounts does not matter.

To find g(f(x)), we can substitute the expression for f(x) into the function g(x):

g(f(x)) = g(x-200) = 0.7(x-200) = 0.7x - 140


Either way, we can see that the price of the computer after both discounts are applied is a function of the original price x, and can be represented by the composition of the functions f and g.

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Answer:

$2.23

Step-by-step explanation:

To find the cost of the bottle of water, we need to subtract the amount of change that Angie received from the twenty-dollar bill that she used to pay. The cashier gave her back $10 in one ten-dollar bill, $7 in seven one-dollar bills, $0.75 in three quarters, and $0.02 in two pennies.

Therefore, the total change that Angie received was: $10 + $7 + $0.75 + $0.02 = $17.77

To find the cost of the bottle of water, we need to subtract this amount from the twenty-dollar bill: $20.00 - $17.77 = $2.23

Therefore, the bottle of water cost $2.23.

The given quantity 240 g can be divided as 100 g, 60 g, and 80 g such that the quantities are in the ratio 5: 3: 4.

A ratio is a comparison between two or more quantities that are measured in the same units.

It is often expressed as a fraction or a colon and is used to describe the relative size or amount of one quantity compared to another.

Here we have 240g

We need to divide 240 g into a 5: 3: 4 ratio

Let 5x, 3x, and 4x be the divided parts

=> 5x + 3x + 4x = 240 g

=> 12x = 240 g

=> x = 20 g  

Now calculate the divided parts as follows

5x = 5(20 g) = 100 g

3x = 3(20 g) = 60 g

4x = 4(20 g) = 80 g

Therefore,

The given quantity 240 g can be divided as 100 g, 60 g, and 80 g such that the quantities are in the ratio 5: 3: 4.  

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The expression 0.26 when written as a fraction in its lowest term is 13/50

Based on the question, we have a set of values that can be used in our calculations.

Fraction = 0.26

As a general rule, a fraction can be expressed as a/b

Where

Using the above values as a guide, we have the following expression

Fraction = 0.26

Multiply the fraction by 1

Fraction = 0.26 * 1

Express 1 as 100/100

So, we have

Fraction = 0.26 * 100/100

Evaluate the product of 0.26 and 100

This gives

Fraction = 26/100

Reduce the quotient of 26 and 100 to the lowest terms by dividing by 2

Fraction = 13/50

Hence, the fraction of 0.26 is 13/50

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Step-by-step explanation:

1. R

2. W

3. O

4. RW

5. OW

6 RO

7. RWO

2.

1.UG

2. G

3. MG

4. MU

5. M

6. U

The length of arcs MH and TY in terms of π are 18π cm and 22π cm respectively.

Arc length = (central angle / 360) x (2 x π x radius)

Arc length of sector of circle = (θ/360º) × 2πr

For the sector MRH:

θ = 180° - 72° = 108°

r = 30 cm

Arc length MH = (108°/360º) × 2π × 30 cm

Arc length MH = 9 × 2π cm

Arc length MH = 18π cm.

For the sector MRH:

θ = 72°

r = (25 + 30) cm = 55 cm

Arc length TY = (72°/360º) × 2π × 55 cm

Arc length TY = 1 × 2π × 11 cm

Arc length TY = 22π cm

Therefore, the length of arcs MH and TY in terms of π are 18π cm and 22π cm respectively.

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The step that Jackson made an error when solving the inequality was Step 1 because he did not multiply - 10 by 4.

When solving the inequality, Jackson had the right idea of multiplying the different sides of the equation by 4 in order to get rid of 4 as a denominator.

However, he was to multiply every figure in the equation by 4. He did not do this with the - 10 on the left side of the equation. This meant that Jackson did not convert that number to - 40 which then led to an incorrect inequality.

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According to the question the standard deviation is approximately $9,400.

Standard deviation is a measure of variability or dispersion in a data set. It is a measure of how much the individual data points within a set deviate from the mean. The standard deviation is calculated by taking the square root of the variance and is expressed as the same unit of measurement as the data set.

The standard deviation of pre-tax family incomes when the head of the household has a university degree can be computed using the empirical rule. According to the empirical rule, approximately 68% of the data lies within one standard deviation of the mean, 95% of the data lies within two standard deviations of the mean, and 99.7% of the data lies within three standard deviations of the mean.

Given that 70% of the pre-tax family incomes when the head of the household has a university degree are between $76,300 and $95,100,
we can calculate that the standard deviation is approximately ($95,100 - $76,300) / 2.66 ≈ $9,400.

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The area of the rectangle is 9 square units

First, we need to know the properties of a rectangle. They are;

From the diagram shown, we have that;

Length of the transformed shape(parallelogram to rectangle) = 3 units

Width = 3 units

The formula for the area of a rectangle is expressed as;

Area = lw

Substitute the values

Area = 3(3)

Area = 9 square units

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Since t-value  is less than the critical value, at α = 0.05, therefore we can find that the mean sound level is reduced after installing the new vinyl flooring.

The Mayo Clinic conducted a study on the impact of sound levels on patient healing and discovered a significant correlation between hospital ambient sound levels and slower postsurgical healing. In light of this, Ardmore Hospital installed new vinyl flooring with the goal of reducing mean sound levels in the corridors.

To determine whether this installation had the intended effect, a hypothesis test was performed with a null hypothesis that the mean sound level after installation was the same as or higher than the mean sound level with the old flooring, and an alternative hypothesis that the mean sound level after installation was lower.

A one-tailed t-test was used with a significance level of α = 0.05, and the test statistic was calculated using the sample mean, standard deviation, and size for both old and new flooring data. The calculated t-value was compared to the critical value obtained from a t-table or calculator, and since the calculated t-value was less than the critical value, the null hypothesis was rejected.

Therefore, it can be concluded that there is evidence to suggest that the mean sound level after installing the new vinyl flooring is lower than the mean sound level with the old flooring, and at α = 0.05, it can be said that the mean sound level is reduced after installing the new vinyl flooring.

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The two polygons are similar using the SAS criteria.

A two-dimensional geometric shape with a finite number of sides is called a polygon. A polygon's sides are constructed from segments of straight lines joined end to end. A polygon's line segments are therefore referred to as its sides or edges. The vertex or corners made by two line segments are where an angle is created. A triangle with three sides is an illustration of a polygon. A circle is a planar figure as well, but since it is curved and lacks sides and angles, it is not regarded as a polygon. Hence, we may argue that while all two-dimensional forms are polygons, not all two-dimensional figures are polygons.

For the given polygons we find the scale factor to determine whether the two figures are similar.

The scale factor is given as:

SF = length of original/ length of new image

SF = 4 / 6

SF = 2/3

For the second segment:

SF = 6/9

SF = 2/3

The ratios of the segment are same. Also the angle between the corresponding segments is 86 degrees.

Hence, the two polygons are similar using the SAS criteria.

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Answer:

if we follow the rule using y=mx+c, we would use rise and run so the distance is 3 up and 4 run.

7 total distance i guess.....i hope this helps.

Area of the parallelogram is 15 cm²

Area of the parallelogram:

Given that;

Base of parallelograms = 3 cm

Side of parallelograms = 5.3

Height of parallelograms = 5 cm

Find:

Area of the parallelogram

Computation:

Area of the parallelogram = l × b

Area of the parallelogram = 3 × 5

Area of the parallelogram = 15 cm²

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Answer:13.O 14.M 15. N

Step-by-step explanation:

these are the graphs that represent the situations best

Answer:

b

Step-by-step explanation:

its really easy when u read it multiple of times

The smallest positive integer that is a multiple of 2, 6, and 9 is 18.

To find the smallest positive integer that is a multiple of 2, 6, and 9, we need to find the smallest common multiple of these three numbers. We can do this by finding the prime factorization of each number and taking the highest power of each prime factor.

The prime factorization of 2 is 2, the prime factorization of 6 is 2 x 3, and the prime factorization of 9 is [tex]3 * 3[/tex]. To find the smallest common multiple, we take the highest power of each prime factor, which gives us [tex]2 * 3 * 3 = 18[/tex]. Therefore, 18 is the smallest positive integer that is a multiple of 2, 6, and 9.

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Answer:

6.3829787234%

Step-by-step explanation:

what 5x10 = 50

60x 10 =600

30x1 =30

1x1=1

2x2=4

Answer:

Step-by-step explanation: shyweydehdeecebccecjeejddijde shut the f

The mass of the gold bar of the trapezium shape and a density of 19.3g/cm³ is found to be 8.646 KG.

The volume of the trapezoidal prism will be determined first. V = BL, where B is the area of the trapezoidal face and L is the prism's length, is the formula for the volume of the prism.

We are aware that a trapezoid's area is equal to B = 1/2(6+10). (4)

B = 32 m²

When we enter the formula for volume, V = 32 x 14 V = 448 m³, we know that L is 14 cm.

Divide the mass by the volume to get the density, or D = M/V.

According to values,

19.3 = M/448

M = 8646.4 grams, which is equal to 8.646 grams.

The density is stated to be 19.3 kg/m³. Hence, the gold weighs 8.646 kilos.

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Complete question - The gold bar trapezium has cross-sectional area. Gold has a density of 19. 3 per cm3. Work out the mass of the gold bar. Give your answer in kilograms. The dimension of the trapezium are length = 14cm, parallel sides are 6cm and 10cm nd the height is 4cm.

As seen in the attached picture, the account by Grant and the painting are consistent with each other since they both depict a serious and formal situation.

Ulysses S. Grant was an American general and statesman who served as the 18th President of the United States. He was born in 1822 in Ohio and graduated from the United States Military Academy at West Point in 1843. He served in the Mexican-American War and later became a leading Union general in the American Civil War.

As we compare his account of Lee's rendition and the painting provided, we can conclude that they are indeed consistent. Both show how serious and formal the meeting was. Grant even describes the way Lee was dressed, which is confirmed by the painting.

The picture and the account appear in the attachment below.

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The probability that the point will be in the square is given by P = 63.70 %

The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible

Probability = number of desirable outcomes / total number of possible outcomes

The value of probability lies between 0 and 1

Given data ,

Let the probability that the point will be in the square be P

Now , the radius of the circle r = 1 inch

So , the area of the circle = πr²

The area of circle = 3.14 inches²

Now , the diagonal of the square = 2 inches

So , the area of the square = 2 inches²

And , probability that the point will be in the square P = ( area of the square / area of circle ) x 100

On simplifying , we get

The probability that the point will be in the square P = 2 / 3.14

The probability that the point will be in the square P = 0.6370

The probability that the point will be in the square P = 63.70 %

Hence , the probability is 63.70 %

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The value of the expression is f(g(x)) = f(x^2) = 2(x²) + 1 = 2x² + 1.

A function is composed in mathematics when two functions, f and g, are used to create a new function, h, such that h(x) = g(f(x)). The function of g is being applied to the function of x, in this case. Hence, a function is essentially applied to the output of another function.

Given that,

f(x)=2x+1 and g(x)=x²

To get the composite function we substitute the value of g(x) in the x-value of the function of f(x).

f(g(x)) = f(x^2) = 2(x²) + 1 = 2x² + 1

Hence, the value of the expression is f(g(x)) = f(x^2) = 2(x²) + 1 = 2x² + 1.

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angles of 0°, 30°, 45°, 60°, and 90° are 100 feet, 86.6 feet, 71.4 feet, 50 feet, and 0 feet, respectively.

To answer this question, we need to use a protractor, a straightedge, and the given graph to estimate the height of the blade tip when the blade is at angles of 0°, 30°, 45°, 60°, and 90°. The arc on the graph represents a portion of the blade tip's path. Assume the blade rotates counterclockwise and the blade is at an angle of 0° when the blade tip is directly to the right of the top of the vertical shaft. This position has been labeled as 0° on the graph.

Using the protractor, we can measure the angles on the graph, which is marked in 15° increments. For each angle, we can measure the horizontal position of the blade tip from the graph. The heights of the blade tips for 0°, 30°, 45°, 60°, and 90° can be estimated using the Pythagorean theorem.

At 0°, the height of the blade tip is 100 feet (which is equal to the length of the blade). At 30°, the height of the blade tip is 86.6 feet. At 45°, the height of the blade tip is 71.4 feet. At 60°, the height of the blade tip is 50 feet. At 90°, the height of the blade tip is 0 feet.

Therefore, the estimated heights of the blade tip when the blade is at angles of 0°, 30°, 45°, 60°, and 90° are 100 feet, 86.6 feet, 71.4 feet, 50 feet, and 0 feet, respectively.

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You would have to pay 67% of the original price to buy the coat and  Juan paid 1. 08% of the purchase price as the total bill.

percentage, a relative value indicating hundredth parts of any quantity.

If the coat is on sale for 33% off the original price, then the price you would have to pay is equal to 100% - 33% = 67% of the original price.

So, you would have to pay 67% of the original price to buy the coat.

If Juan paid 8% sales tax on his purchase, then the total bill would be the original price plus 8% of the original price.

Let's say the purchase price of the video game is x.

Then, the sales tax would be 8% of x, which is 0.08x.

So, the total bill that Juan paid is x + 0.08x = 1.08x.

Therefore, Juan paid 1. 08% of the purchase price as the total bill.

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Answer:

Perimeter, in feet, of quadrilateral A'BAC = 2(a + b) feet

Last Option

Step-by-step explanation:

Reflecting a figure does not change its dimensions, only its orientation

Therefore when ΔABC is reflected across the line BC, the reflected image is another triangle ABC with the same dimensions and BC as the common side, B and C points are unchanged and A is reflected to A'

Therefore the quadrilateral ABCA' will have sides a and b

Perimeter of a quadrilateral = 2 x (sum of sides)

= 2(a + b)

This is the last answer choice

See figure  for an understanding

We can see here that the an expression for the perimeter, in feet,

of quadrilateral A'BAC will be: E. 2(a + b).

Perimeter is the total length of the boundary of a two-dimensional geometric shape, such as a polygon or a circle. It is the distance around the shape and is measured in units such as centimeters, meters, feet, or yards.

We see here that the above option is correct. It should be noted that as the image is reflected across side BC, the dimensions didn't change. Thus, the reflected image alongside the triangle gives a quadrilateral.

The perimeter of a quadrilateral = sum of all the sides of a quadrilateral.

Thus, for  quadrilateral A'BAC, the perimeter = a + a + b + b = 2a + 2b = 2(a + b).

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The length of the side x in the triangle is approximately 7.5.

A right-angled triangle is a geometric shape that consists of three sides and three angles. One of the angles in a right-angled triangle measures 90 degrees, which is called a right angle. The side opposite to the right angle is called the hypotenuse, and the other two sides are called the legs or catheti.

The Pythagorean theorem is a fundamental property of right-angled triangles that states that the sum of the squares of the two shorter sides (legs) is equal to the square of the hypotenuse. This can be written as:

a² + b² = c²

where a and b are the lengths of the legs, and c is the length of the hypotenuse.

Right-angled triangles also have many real-world applications, such as in construction, engineering, architecture, and navigation. They are used to calculate distances, heights, angles, and other measurements in many different contexts.

Using trigonometry, we can solve for x:

sin(32°) = x/14

x = 14 * sin(32°)

x ≈ 7.5 (rounded to the nearest tenth)

Therefore, the length of the side x in the triangle is approximately 7.5.

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The dimensions of the poster are 2 inches by 15 inches.

Algebra is a branch of mathematics that deals with symbols and the rules for manipulating these symbols. It is used to solve problems and represent mathematical relationships and formulas. In algebra, letters and other symbols are used to represent numbers and quantities, allowing us to express mathematical relationships and patterns in a more general and abstract way.  Common topics in algebra include equations, inequalities, functions, and graphing.

An equation is a mathematical statement that shows that two expressions are equal. Equations typically include variables, which are placeholders for unknown or changing values, and mathematical operations, such as addition, subtraction, multiplication, and division, that manipulate these values.

In the given question,

Let's use algebra to solve for the dimensions of the poster.

Let w be the width of the poster in inches. Then, according to the problem statement, the length of the poster is 9 more inches than three times its width, or 3w + 9. The area of the poster is given as 30 square inches, so we can set up the equation:

A = lw = (3w + 9)w = 30

Expanding the right-hand side and simplifying, we get:

3w^2 + 9w - 30 = 0

Dividing both sides by 3, we obtain:

w^2 + 3w - 10 = 0

This is a quadratic equation that we can solve using factoring or the quadratic formula. Factoring, we can write:

(w + 5)(w - 2) = 0

This gives us two solutions: w = -5 and w = 2. Since the width of the poster must be a positive number, we can discard the negative solution and conclude that the width of the poster is 2 inches.

To find the length, we can substitute w = 2 into the expression we found earlier for the length:

l = 3w + 9 = 3(2) + 9 = 15

Therefore, the dimensions of the poster are 2 inches by 15 inches.

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